Math 322 -- Mathematical Analysis for Engineers
- Practice problems for Exam 2 (some of these were assigned as homework problems): * 7.8 Matrix inverses # 1--10 * 7.7 Determinants # 7--15 * 7.4 Linear independence, rank, vector space # 1--10, 17--25, 27, 30, 32, 33 * 1.1 First-order linear ODEs # 1--8 * 2.2 Homogeneous linear ODEs w/ const coeffs # 1--15 * 8.1 Eigenvalues and eigenvectors # 1--16 * 8.4 Diagonalization # 9--16 You are also responsible for knowing how to solve problems similar to those I assigned as homework, even if they are not in the text. For example, you should know how to do problems like this one. - HW9 due Wed 3/25This page was last updated on .Thu 3/268.1: #1, 2, 3, 4, 5, *10, *12 8.4: #9, 10, 11, 13, *14 - HW8 due Wed 3/11: 7.4: #4, 6, *7 Read 7.4, 7.5 In addition to bases for the row and column spaces, also find a basis for the null space. 1.1: #17, 18 2.2: #1, 2, 3, 4, 5, 6, *14 For #14, find the solution with y(0) = y'(0) = 1. Also write up this problem. - HW7 dueWed 3/4Fri 3/6: 7.4: #1, *3, 9, *17, 18, 19, 20, *27, 30, *31(I may add a couple more problems to this set.)- HW6 due Wed 2/25 (write-up due Mon 3/2) 7.7: #11, 12, *13, 14, *15 For 13-15, do it by both "cofactor expansions" (the general definition I gave in class) AND by row reduction to row echelon form.7.4: #17, 18, 19, 20: I'll re-assign these for next week. - HW5 due Fri 2/20: 7.8: #1, 2, 3, 4, 5, 12, 15 (*) Problem: Let A be the matrix -1 - 2i 3 - 1i -1 - 1i 0 + 2i 2 - 3i 0 + 1i 3 + 3i 0 + 0i 2 + 1i Find the inverse of A. 7.7: #7, 8 Read 7.7, 7.8 (I'm still planning to have a quiz on Friday.) - Some practice problems for exam 1: 13.1: #3, 5, 11, 13, 15, 17, 19 13.2: #7, 9, 11, 13, 17, 21, 23, 25, 27 13.5: #3, 5, 7, 17 13.6: #1, 9, 15 13.7: #15, 19, 21 7.1: #13, 15 7.2: #13, 15, 17 7.3: #9, 11, 13 (Some of the questions in 7.2 involve transposition, which we did not discuss in class but is part of your reading. It is very easy; just read the text.) - HW4 due Thu 2/12 at 5pm: 7.3: #4, 5*, 6*, 7, 10 For each problem, in addition to solving the linear system represented by the augmented matrix, also do the following: (i) Find the reduced row echlon form of the matrix. (ii) Describe the geometry of the solution set -- is it a point, a line, or something else, and if so what? 7.2: read up to and including transposition 7.2: #11, 18 - HW3 due Wed 2/4: 7.1: #8, 9, 10, 11 7.3: #1, 3, *8, *13, *14 Problem: Solve the system of equations represented by the following 2x3 augmented matrix 1 -2 - 3i 3 - 2i -3 + 3i 16 + 3i -4 + 14i - HW2 due Wed 1/28: 13.6: #3 6 7 8 11 12 13.7: #5 6 7 8 11 12 13 14 18 - HW1 due Wed 1/21: 13.1: #1, 2, 9, 12 13.2: #1, 2, 3, 5, 15, 21 13.5: #2, 9, 15